Book an excursion if going to Falmouth! There is not much to do in the port at this time that you can't do in any other port and you can see it all in about 45 minutes, tops!
I love Nassau because even if you've been here 100 times you can always find something new to do or try. Check the port specific boards here for good tips on Nassau to find the right thing for you and your budget. It runs the gamut here from free to $$$$$ and from relaxed to P-A-R-T-Y.